Problem: $\dfrac{1}{9} \div \dfrac{9}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{9}{5}$ is $\dfrac{5}{9}$ Therefore: $ \dfrac{1}{9} \div \dfrac{9}{5} = \dfrac{1}{9} \times \dfrac{5}{9} $ $ \phantom{\dfrac{1}{9} \times \dfrac{5}{9}} = \dfrac{1 \times 5}{9 \times 9} $ $ \phantom{\dfrac{1}{9} \times \dfrac{5}{9}} = \dfrac{5}{81} $